The invention described herein relates to structural members. In most buildings, these are beams, columns, and struts. Structural members are employed to transmit forces in compression, tension, shear, bending, torsion and any combination thereof.
In order to accomplish such transmission, a suitable material is selected and a cross-sectional shape of the member is selected. Properties of the material selected influence the choice of cross-sectional shape and vice-versa.
In addition to this mutual influence, there are features of cross-sectional shape which have similar effects on all materials. These features relate to the mode of transmission of the force applied. The shapes generally used in current practice achieve popularity by providing a measure of efficiency of material used while transmitting force in some combination of the modes cited. A particular shape which especially favors one mode of transmission may not favor transmission of force in the other modes. It is desired to discover a shape which achieves very good transmission of force in a combination of modes while maintaining efficiency of material used.
The distribution of material over the cross-section of the member required to transmit a given force is determined by the factors governing the failure of the material or member in the mode of force transmission employed. In compression, the material may fail by crushing or the member which the material composes may fail by buckling. The former is discouraged by increasing the cross-sectional area subjected to the compressive force. The latter is discouraged by symmetrically distributing the cross-sectional area at a distance from the centroid of the area. An equilateral triangular distribution has been suggested for the transmission of pure axial compression in Archive for Rational Mechanics and Analysis, Vol. 5, No. 4, 1960, pp. 275-285, "The Shape of the Strongest Column", Joseph B. Keller, communicated by C. Truesdell and Product Engineering, Aug. 29, 1966, pp. 97-102, "Odd shapes and materials save weight in structures", Nicholas P. Chironis.
In tension, the material may fail by splitting or tearing. Such failure is encouraged by the formation of sharp radii in the material. Such failure is discouraged by increasing the cross-sectional area subjected to the tensile force and the maintenance of large radius boundaries of the cross-sectional shape of the member.
In shear, the material may fail by splitting or tearing as in tension. Such failure is discouraged by the techniques suggested with regard to tension. The avoidance of sharp radii promotes a smooth flow of shear stress over the cross-sectional shape thereby discouraging failure of the material.
In bending, the material of which the member is composed is subjected to both compression and tension. These modes of transmission occur in distinct zones of the cross-sectional shape of the member. The interface between these zones is called the neutral axis. In the case of an I-beam supported at its opposite ends and a downward load at its center, compression occurs in the upper portion and tension occurs in the lower portion. The shape of the compression zone must discourage compressive failure. The shape of the tension zone must discourage tensile failure. The magnitudes of the compressive and tensile forces in pure bending are inversely related to the distance of the centroid of the specific zone from the neutral axis. It is advantageous, therefore, to have a compression zone and a tension zone whose centroids are displaced from the neutral axis.
In bending, the material of which the member is composed is also subjected to shear. Transmission of force in this mode additionally requires that the cross-sectional shapes of the compressive and tension zones have no sharp radii and be connected in such manner as to promote a smooth flow of shear stress over the entire cross-sectional shape.
In torsion, the material of which the member is composed is subjected to both tension and shear. The magnitudes of the tensile and shear forces in pure torsion are inversely related to the distance of the force transmitting material from the axis of applied torque. It is advantageous to arrange the force transmitting material symmetrically about this axis in a continuous shape thereby forming a tube.
A single cross-sectional shape which satisfies the above criteria would be especially useful where combinations of force transmission modes are required. Most structures present such a requirement. In buildings, beams are required to transmit forces in the following descending hierarchy of modes: bending, shear, torsion, tension, compression. Columns are required to transmit forces in the following descending hierarchy of modes: compression, bending, shear, torsion, tension. Other structures involve other-named members which present other hierarchies of force transmission requirements.
Reinforcing elements such as steel rods have been previously used in concrete structures. The use of secondary meshes with such reinforcing elements is disclosed in U.S. Pat. No. 1,233,053 issued July 10, 1917 to R. B. Harinian.
In the construction of a building, non-structural elements as electrical wiring, plumbing, ventilation, sprinkler systems and the like are commonly installed by separate trades in conduits which are separate and distinct from the structural members. In U.S. Pat. No. 2,809,074 issued Oct. 8, 1957 to J. L. McDonald, it has been proposed to use a metal pipe component in a metallic structural unit as a conduit for a fire extinguisher system.